The fax from Pyongyang on Thursday threatened to launch a strike against the South "without notice." The strikes would be launched "mercilessly" if "the provocation against our highest dignity is to be repeated in the downtown of Seoul."
In response to the faxed threat, South Korea told the North that it would "sternly react" to any provocations.
At the anti-Pyongyang rallies in Seoul, some protesters reportedly burned photographs of Kim Jong-un.
Threats from North Korea occur regularly following perceived provocations by South Korea.